Volumes for rogue waves of coupled equations

Abstract

Rogue waves can appear in various physical scenarios, including those described by coupled equations. Volumes for rogue wave pairs of coupled equations can be defined using intensities of each individual rogue wave, or via a combined definition for the pair. We consider Manakov equations supporting bright-dark rogue wave pairs, and various other equations. This extends the rogue wave ‘volume’ concept in a useful way and allows for characterization of these pairs by using a single number. If the volume is found from experimental data, e.g. in a water tank, then the values of internal solution parameters can be deduced.